Several realistic situations in vehicular traffic that give rise to queues can be modeled through conservation laws with boundary and unilateral constraints on the flux. This paper provides a rigorous analytical framework for these descriptions, comprising stability with respect to the initial data, to the boundary inflow and to the constraint. We present a framework to rigorously state optimal management problems and prove the existence of the corresponding optimal controls. Specific cases are dealt with in detail through ad hoc numerical integrations. These are here obtained implementing the wave front tracking algorithm, which appears to be very precise in computing, for instance, the exit times.

Keywords: optimal control of conservation laws, constrained hyperbolic pdes, traffic modelling

@article{M2AN_2011__45_5_853_0, author = {Colombo, Rinaldo M. and Goatin, Paola and Rosini, Massimiliano D.}, title = {On the modelling and management of traffic}, journal = {ESAIM: Mathematical Modelling and Numerical Analysis }, pages = {853--872}, publisher = {EDP-Sciences}, volume = {45}, number = {5}, year = {2011}, doi = {10.1051/m2an/2010105}, mrnumber = {2817547}, zbl = {1267.90032}, language = {en}, url = {http://www.numdam.org/articles/10.1051/m2an/2010105/} }

TY - JOUR AU - Colombo, Rinaldo M. AU - Goatin, Paola AU - Rosini, Massimiliano D. TI - On the modelling and management of traffic JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2011 SP - 853 EP - 872 VL - 45 IS - 5 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an/2010105/ DO - 10.1051/m2an/2010105 LA - en ID - M2AN_2011__45_5_853_0 ER -

%0 Journal Article %A Colombo, Rinaldo M. %A Goatin, Paola %A Rosini, Massimiliano D. %T On the modelling and management of traffic %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2011 %P 853-872 %V 45 %N 5 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an/2010105/ %R 10.1051/m2an/2010105 %G en %F M2AN_2011__45_5_853_0

Colombo, Rinaldo M.; Goatin, Paola; Rosini, Massimiliano D. On the modelling and management of traffic. ESAIM: Mathematical Modelling and Numerical Analysis , Volume 45 (2011) no. 5, pp. 853-872. doi : 10.1051/m2an/2010105. http://www.numdam.org/articles/10.1051/m2an/2010105/

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